A novel way to solve the D _q -appell equation

We develop and implement a novel approach for determining the q-orthogonal polynomial solutions to the D _q -Appell Equation (D _q P _n (x) = γ _n P _n−1 (x)), where D _q is the Askey-Wilson divided-difference operator, and γ _n is a function of n and q that is independent of x. More specifically, our methodology relies only on the second and third coeffi cients of P _n (x) and a three-term recurrence relation. Together, these structures lead to various difference equations from which recursion coeffi cients can be inferred. Moreover, this approach has the potential to be applied to other types of characterization problems as well.